Abstract

Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. The core step of the KDD process is the application of a Data Mining algorithm in order to produce a particular enumeration of patterns and relationships in large databases. Clustering is one of the major data mining techniques and aims at grouping the data objects into meaningful classes (clusters) such that the similarity of objects within clusters is maximized, and the similarity of objects from different clusters is minimized. This can serve to group customers with similar interests, or to group genes with related functionalities.
Currently, a challenge for clustering-techniques are especially high dimensional feature-spaces. Due to modern facilities of data collection, real data sets usually contain many features. These features are often noisy or exhibit correlations among each other. However, since these effects in different parts of the data set are differently relevant, irrelevant features cannot be discarded in advance. The selection of relevant features must therefore be integrated into the data mining technique.
Since about 10 years, specialized clustering approaches have been developed to cope with problems in high dimensional data better than classic clustering approaches. Often, however, the different problems of very different nature are not distinguished from one another. A main objective of this thesis is therefore a systematic classification of the diverse approaches developed in recent years according to their task definition, their basic strategy, and their algorithmic approach. We discern as main categories the search for clusters (i) w.r.t. closeness of objects in axis-parallel subspaces, (ii) w.r.t. common behavior (patterns) of objects in axis-parallel subspaces, and (iii) w.r.t. closeness of objects in arbitrarily oriented subspaces (so called correlation cluster).
For the third category, the remaining parts of the thesis describe novel approaches. A first approach is the adaptation of density-based clustering to the problem of correlation clustering. The starting point here is the first density-based approach in this field, the algorithm 4C. Subsequently, enhancements and variations of this approach are discussed allowing for a more robust, more efficient, or more effective behavior or even find hierarchies of correlation clusters and the corresponding subspaces. The density-based approach to correlation clustering, however, is fundamentally unable to solve some issues since an analysis of local neighborhoods is required. This is a problem in high dimensional data. Therefore, a novel method is proposed tackling the correlation clustering problem in a global approach. Finally, a method is proposed to derive models for correlation clusters to allow for an interpretation of the clusters and facilitate more thorough analysis in the corresponding domain science. Finally, possible applications of these models are proposed and discussed.